Colleges where a specific major or division is more selective do it that way because that specific major or division is filled to capacity. Different STEM majors may be in different divisions (e.g. biology in the arts and science division, mechanical engineering in the engineering division) that have different admission selectivity; if the school admits by major, different STEM majors may have different admission selectivity.
Note that three out of the eight Ivy League schools (Columbia, Cornell, Penn) admit by division.
Yes, put down the intended major. If admission selectivity does differ, then changing major after enrolling could involve another competitive admission process.